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Given
a
Takagi–Sugeno
(TS)
system,
this
paper
proposes
a
novel
methodology
to
obtain
the
state
feedback
controller
guar-
anteeing,
asymptotically
as
a
Polya-related
complexity
parameter
grow ... [+]

Given
a
Takagi–Sugeno
(TS)
system,
this
paper
proposes
a
novel
methodology
to
obtain
the
state
feedback
controller
guar-
anteeing,
asymptotically
as
a
Polya-related
complexity
parameter
grows,
the
largest
(membership-shape
independent)
possible
domain-of-attraction
with
contraction-rate
performance
λ
,
based
on
polyhedral
λ
-contractive
sets
from
constrained
linear
systems
literature.
The
resulting
controller
is
valid
for
any
realisation
of
the
memberships,
as
usual
in
most
TS
literature.
For
a
finite
com-
plexity
parameter,
an
inner
estimate
of
such
largest
set
is
obtained;
the
frontier
of
such
approximation
can
be
understood
as
the
level
set
of
a
polyhedral
control-Lyapunov
function.
Convergence
of
a
proposed
iterative
algorithm
is
asymptotically
necessary
and
sufficient
for
TS
system
stabilisation:
for
a
high-enough
value
of
the
complexity
parameter,
any
conceivable
shape-independent
Lyapunov
controller
design
procedure
will
yield
a
proven
domain
of
attraction
smaller
or
equal
to
the
algorithm’s
output. [-]